= Solution
Combine the real variables into $z=x+iy$. The <linear system of ordinary differential equations> becomes $z'=(1-i\mu)z$, hence $z=(A+iB)e^{(1-i\mu)t}$ for arbitrary real $A,B$. Taking real and imaginary parts gives
$$
\boxed{x=e^t(A\cos\mu t+B\sin\mu t),\qquad y=e^t(-A\sin\mu t+B\cos\mu t).}
$$
The two independent constants cover every real initial condition. In the <phase plane>, the distance from the origin grows as $e^t$ and the polar angle changes at rate $-\mu$. For $\mu\ne0$ the trajectories are outward <logarithmic spirals>; for $\mu=0$ they are outward straight rays.
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